Q.1. Define “Statistics”. What are the functions of Statistics?

Distinguish between Primary data and Secondary data.

ANS:

STATISTICS:

Statistics plays an important role in almost every facet of human

life. In the business context, managers are required to justify

decisions based on data.

They need statistical models to support these decisions.

Statistical skills enable managers to collect, analyze and

interpret data and make relevant decisions. Statistical concepts

and statistical thinking enable them to:

Solve problems in almost any domain

Support their decisions

Reduce guesswork

Due to advanced communication network, rapid changes in

consumer behavior, varied expectations of variety of consumers

and new market openings, modern managers have a difficult

task of making quick and appropriate decisions.

Therefore, there is a need for them to depend more upon

quantitative techniques like mathematical models, statistics,

operations research and econometrics.

Functions of Statistics:

Statistics is used for various purposes. It is used to simplify

mass data and to make comparisons easier. It is also used to

bring out trends and tendencies in the data as well as the hidden

relations between variables. All this helps to make decision

making much easier.

Statistics simplifies mass data The use of statistical concepts

helps in simplification of complex data. Using statistical

concepts, the managers can make decisions more easily. The

statistical methods help in reducing the complexity of the data

and consequently in the understanding of any huge mass of

data.

Statistics makes comparison easier Without using statistical

methods and concepts, collection of data and comparison cannot

be done easily. Statistics helps us to compare data collected

from different sources. Grand totals, measures of central

tendency, measures of dispersion, graphs and diagrams,

coefficient of correlation all provide ample scopes for comparison

Statistics brings out trends and tendencies in the data

After data is collected; it is easy to analyze the trend and

tendencies in the data by using the various concepts of

Statistics.

Statistics brings out the hidden relations between

variables Statistical analysis helps in drawing inferences on

data. Statistical analysis brings out the hidden relations between

variables.

Decision making power becomes easier With the proper

application of Statistics and statistical software packages on the

collected data, managers can take effective decisions, which can

increase the profits in a business.

Primary data :

Data collected for the first time keeping in view the objective of

the survey is known as primary data. They are likely to be more

reliable. However, cost of collection of such data is much higher.

Primary data is collected by the census method. In other words,

information with respect to each and every individual of the

population is observed.

Collection of primary data can be done by any of the following

methods.

1. Direct personal observation

2. Indirect oral interview

3. Information through agencies

4. Information through mailed questionnaires

5. Information through schedule filled by investigators

Secondary data:

Any information, that is used for the current investigation but is

obtained from some data, which has been collected and used by

some other agency or person in a separate investigation, or

survey, is known a secondary data. They are available in

published or unpublished form.

In published form, secondary data is available in research

papers, news papers, magazines, government publication,

international publication, and websites. Secondary data is

collected for different purposes. Therefore, care should be

exercised while making use of it.

The accuracy, reliability, objectives and scope of secondary data

should be examined thoroughly before use. Secondary data may

be collected either by census or by sampling methods.

The various sources of published data are:

Reports and official publications of international and

national organizations as well as central and state

governments

Publications of several local bodies such as municipal

corporations and district boards

Financial and economic journals

Annual reports of various companies

Differences between primary and secondary data

Primary Data Secondary Data

1. Data is original and 1. Data is not reliable.

thus more accurate and

reliable.

2. Gathering data is

expensive.

2. Gathering data is cheap

3. Data is not easily

accessible.

3. Data is easily

accessible through

internet or other

resources.

4. Most of the data is

homogeneous.

4. Data is not

homogeneous.

5. Collection of data

requires more time.

5. Collection of data

requires less time.

6. Extra precautionary

measures need not be

taken.

6. Data needs extra care.

7. Data gives detailed

information.

7. Data may not be

adequate

Q.2. Draw a histogram for the following distribution:

Age 0-10 10-20 20-30 30-40 40-50

No. of

people

2 5 10 8 4

ANS:

Q3. Find the

(i) Arithmetic mean and

(ii) The median value of the following set of values: 40, 32, 24,

36, 42, 18, 10.

ANS:

(i) Arithmetic Mean:

= (40 + 32 + 24 + 36 + 42 + 18 + 10) / 7

= 202/7

=28.85

(ii) Median:

= [ (n+1)/2 ]th Value

Here, n = no. of values = 7

Median = [ (7+1)/2 ]th Value = 8/2

= 4th value

4th value= 36

Q4. Calculate the standard deviation of the following data:

Marks 78-80 80-82 82-84 84-86 86-88 88-90

No. Of

student

s

3 15 26 23 9 4

ANS:

Marks (X) No. Of Students (F) Mid Value of (X)=M M- Assumed Mean= D D 2 (F*D) 2

78-80 3 79 -5 25 75

80-82 15 81 -3 9 135

82-84 26 83 -1 1 26

84-86 23 85 1 1 23

86-88 9 87 3 9 81

88-90 4 89 5 25 100

80 504 440

Assumed mean = 504/6 = 84

Standard deviation= Square root of [sum of all: (F*D) 2 / sum of all

frequencies]

= Square root of 440/80

= Square root of 5.4

ANS= 2.34

Q.5. Explain the following terms with respect to Statistics:

(i) Sample,

(ii) Variable,

(iii) Population.

ANS:

SAMPLE:

A sample is a part or subset of the population. By studying the

sample, you can predict the characteristics of the entire

population from where the sample is taken. The data that

describes the characteristics of a sample is known as statistic.

If the population is large, it is hard to collect data. Hence, a part

of the population is chosen to study the characteristics of the

entire population. The size of the sample can never be as large

as the size of the population. Proper care must be taken while

choosing the samples.

POPULATION:

The totality of all units or individuals in a survey is called population or

universe. If the number of objects in a population is finite then it is

called finite population otherwise it is known as infinite population.

constitutes the entire population.

VARIABLE:

In a population, some characteristics remain the same for all

units and some others vary from unit to unit. The quantitative

characteristic that varies from unit to unit is called a variable.

The qualitative characteristic that varies from unit to unit is

called an attribute.

A variable that assumes only some specified values in a given

range is known as discrete variable. A variable that assumes all

the values in the range is known as continuous variable.

For example, the number of children per family and number of

petals in a flower are examples of discrete variables. The height

and weight of persons are examples of continuous variables.

Q.6. An unbiased coin is tossed six times. What is the

probability that the tosses will result in:

(i) At least four heads, and

(ii) Exactly two heads.

ANS:

BASIC TERMS:

Total outcomes = 6= N

Required event = X

Favorable outcomes= P

Unfavorable outcomes= Q

Here outcome will be either Head or Tail,

So outcome for single success or failure is = 1/2

(i) At least four Heads:

Event is X

Here we’ll find out P(X>=4) using binomial distribution

P(X=r) = nCr * (P)r * (Q)n-r

P(X>=4)= P(X=4)+ P(X=5)+ P(X=6)

Here,

P(X=4) = 6C4 * (1/2)4 * (1/2)6-4 = 15 * (1/2)6 = 0.2343

P(X=5) = 6C5 * (1/2)5 * (1/2)6-5 = 6 * (1/2)6 = 0.0937

P(X=6) = 6C6 * (1/2)6 * (1/2)6-6 = 1 * (1/2)6 = 0.0156

ANS= 0.3436

(ii) Exactly two heads:

Event is X

Here we’ll find out P(X=2) using binomial distribution

P(X=r) = nCr * (P)r * (Q)n-r

Here, n=6 , r=2 P=Q= success= Failure= 1/2

P(X=2) = 6C2 * (1/2)2 * (1/2)6-2 = 15 * (1/2)6

ANS=0.2343